On fuzzy convexity and parametric fuzzy optimization
Fuzzy Sets and Systems
Fuzzy multiple objective programming and compromise programming with Pareto optimum
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Fuzzy logic: intelligence, control, and information
Fuzzy logic: intelligence, control, and information
Some properties of convex fuzzy sets and convex fuzzy cones
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Pareto-optimality of compromise decisions
Fuzzy Sets and Systems
A property on convex fuzzy sets
Fuzzy Sets and Systems
Fuzzy convexity and multiobjective convex optimization problems
Computers & Mathematics with Applications
Φ1-concavity and fuzzy multiple objective decision making
Computers & Mathematics with Applications
On characterizations of preinvex fuzzy mappings
Computers & Mathematics with Applications
Preincavity and fuzzy decision making
Fuzzy Sets and Systems
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Since almost all practical problems are fuzzy and approximate, fuzzy decision making becomes one of the most important practical approaches. One off the important aspects for formulating and for solving fuzzy decision problems is the concept of convexity. In this paper, we investigate the interrelationships of several concepts of generalized convex fuzzy sets. We also prove that, in the upper semicontinuous case, the class of semistrictly quasi-convex fuzzy sets lies between the convex and quasi-convex classes. Aggregation or composition is an essential part for optimization or modeling, and some important composition rules for upper semicontinuous fuzzy sets are developed. We prove that a convex combination of upper semicontinuous fuzzy sets is an upper semicontinuous fuzzy set and the intersection of finitely many upper semicontinuous fuzzy sets is an upper semicontinuous fuzzy set. Finally, the criteria for the existence of fuzzy decision under upper semicontinuity conditions are derived and two examples in multiple objective programming are used to illustrate the approach.